Showing papers on "Job shop scheduling published in 1999"

Heuristic algorithms for the resource-constrained project scheduling problem: classification and computational analysis

Abstract: The resource-constrained project scheduling problem (RCPSP) can be given as follows. A single project consists of a set J = {0,1,…, n, n +1} of activities which have to be processed. Fictitious activities 0 and n + 1 correspond to the “project start” and to the “project end”, respectively. The activities are interrelated by two kinds of constraints. First, precedence constraints force activity j not to be started before all its immediate predecessor activities comprised in the set P j have been finished. Second, performing the activities requires resources with limited capacities. We have k resource types, given by the set K = {1,…,K}. While being processed, activity j requires r j,k units of resource type k ∈ K during every period of its non-preemptable duration p j . Resource type k has a limited capacity of R k at any point in time. The parameters pj,r j,k , and R k are assumed to be deterministic; for the project start and end activities we have pj = 0 and r j,k = 0 for all k ∈ K. The objective of the RCPSP is to find precedence and resource feasible completion times for all activities such that the makespan of the project is minimized. Figure 7:1 gives an example of a project comprising n = 6 activities which have to be scheduled subject to K = 1 renewable resource type with a capacity of 4 units. A feasible schedule with an optimal makespan of 13 periods is represented in Figure 7:2.

Scheduling with time dependent processing times: Review and extensions

Abstract: In classical scheduling theory job processing times are constant However, there are many situations where processing time of a job depends on the starting time of the job in the queue This paper reviews the rapidly growing literature on single machine scheduling models with time dependent processing times Attention is focused on linear, piecewise linear and non-linear processing time functions for jobs We survey known results and introduce new solvable cases Finally, we identify the areas and give directions where further research is needed

A tutorial survey of job-shop scheduling problems using genetic algorithms, part II: hybrid genetic search strategies

Abstract: Job-shop scheduling problem is one of the well-known hardest combinatorial optimization problems. During the last three decades, this problem has captured the interest of a significant number of researchers. A lot of literature has been published, but no efficient solution algorithm has been found yet for solving it to optimality in polynomial time. This has led to recent interest in using genetic algorithms to address the problem. How to adapt genetic algorithms to the job-shop scheduling problems is very challenging but frustrating. Many efforts have been made in order to give an efficient implementation of genetic algorithms to the problem. During the past decade, two important issues have been extensively studied. One is how to encode a solution of the problem into a chromosome so as to ensure that a chromosome will correspond to a feasible solution. The other issue is how to enhance the performance of genetic search by incorporating traditional heuristic methods. Because the genetic algorithms are not well suited for fine-tuning of solutions around optima, various methods of hybridization have been suggested to compensate for this shortcoming. The purpose of the paper is to give a tutorial survey of recent works on various hybrid approaches in genetic job-shop scheduling practices. The research on how to adapt the genetic algorithms to the job-shop scheduling problem provide very rich experiences for the constrained combinatorial optimization problems. All of the techniques developed for the problem are very useful for other scheduling problems in modern flexible manufacturing systems and other difficult-to-solve combinatorial optimization problems.

Production scheduling and rescheduling with genetic algorithms

Abstract: A general model for job shop scheduling is described which applies to static, dynamic and non-deterministic production environments. Next, a Genetic Algorithm is presented which solves the job shop scheduling problem. This algorithm is tested in a dynamic environment under different workload situations. Thereby, a highly efficient decoding procedure is proposed which strongly improves the quality of schedules. Finally, this technique is tested for scheduling and rescheduling in a non-deterministic environment. It is shown by experiment that conventional methods of production control are clearly outperformed atreasonable runtime costs.

Power optimization of variable-voltage core-based systems

Abstract: The growing class of portable systems, such as personal computing and communication devices, has resulted in a new set of system design requirements, mainly characterized by dominant importance of power minimization and design reuse. The energy efficiency of systems-on-a-chip (SOC) could be much improved if one were to vary the supply voltage dynamically at run time. We developed the design methodology for the low-power core-based real-time SOC based on dynamically variable voltage hardware. The key challenge is to develop effective scheduling techniques that treat voltage as a variable to be determined, in addition to the conventional task scheduling and allocation. Our synthesis technique also addresses the selection of the processor core and the determination of the instruction and data cache size and configuration so as to fully exploit dynamically variable voltage hardware, which results in significantly lower power consumption for a set of target applications than existing techniques. The highlight of the proposed approach is the nonpreemptive scheduling heuristic, which results in solutions very close to optimal ones for many test cases. The effectiveness of the approach is demonstrated on a variety of modern industrial strength multimedia and communication applications.

Heavy traffic resource pooling in parallel-server systems

Abstract: We consider a queueing system with r non-identical servers working in parallel, exogenous arrivals into m different job classes, and linear holding costs for each class Each arrival requires a single service, which may be provided by any of several different servers in our general formulations the service time distribution depends on both the job class being processed and the server selected The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs onto available servers A linear program involving only first-moment data (average arrival rates and mean service times) is used to define heavy traffic for a system of this form, and also to articulate a condition of overlapping server capabilities which leads to resource pooling in the heavy traffic limit Assuming that the latter condition holds, we rescale time and state space in standard fashion, then identify a Brownian control problem that is the formal heavy traffic limit of our rescaled scheduling problem Because of the assumed overlap in server capabilities, the limiting Brownian control problem is effectively one-dimensional, and it admits a pathwise optimal solution That is, in the limiting Brownian control problem the multiple servers of our original model merge to form a single pool of service capacity, and there exists a dynamic control policy which minimizes cumulative cost incurred up to any time t with probability one Interpreted in our original problem context, the Brownian solution suggests the following: virtually all backlogged work should be held in one particular job class, and all servers can and should be productively employed except when the total backlog is small It is conjectured that such ideal system behavior can be approached using a family of relatively simple scheduling policies related to the c\mu rule

Minimizing makespan on a single batch processing machine with dynamic job arrivals

Abstract: We consider the problem of minimizing makespan Cmax on a single batch processing machine in the presence of dynamic job arrivals. The batch processing machine can process up to B jobs simultaneously. The processing time of a batch is given by the processing time of the longest job in the batch. We present polynomial and pseudopolynomial-time algorithms for several special cases, develop efficient heuristics for the general problem and evaluate their performance through extensive computational experiments. Our results indicate that several of the heuristics have an excellent average performance with a modest computational burden.

Genetic scheduling for parallel processor systems: comparative studies and performance issues

Abstract: Task scheduling is essential for the proper functioning of parallel processor systems. Scheduling of tasks onto networks of parallel processors is an interesting problem that is well-defined and documented in the literature. However, most of the available techniques are based on heuristics that solve certain instances of the scheduling problem very efficiently and in reasonable amounts of time. This paper investigates an alternative paradigm, based on genetic algorithms, to efficiently solve the scheduling problem without the need to apply any restricted assumptions that are problem-specific, such is the case when using heuristics. Genetic algorithms are powerful search techniques based on the principles of evolution and natural selection. The performance of the genetic approach will be compared to the well-known list scheduling heuristics. The conditions under which a genetic algorithm performs best will also be highlighted. This will be accompanied by a number of examples and case studies.

On combinatorial auction and Lagrangean relaxation for distributed resource scheduling

Abstract: Most existing methods for scheduling are based on centralized or hierarchical decision making using monolithic models. In ihis study, we investigate a new method based on a distributed and locally autonomous decision structure using the notion of combinatorial auction. In combinatorial auction the bidders demand a combination of dependent objects with a single bid. We show that not only can we use this auction mechanism to handle complex resource scheduling problems, but there exist strong links between combinatorial auction and Lagrangean-based decomposition. Exploring some of these properties, we characterize combinatorial auction using auction protocols and payment functions. This study is a first step toward developing a distributed scheduling framework that maintains system-wide performance while accommodating local preferences and objectives. We provide some insights to this framework by demonstrating four different versions of the auction mechanism using job shop scheduling problems.

Stochastic load balancing and related problems

Abstract: We study the problems of makespan minimization (load balancing), knapsack, and bin packing when the jobs have stochastic processing requirements or sizes. If the jobs are all Poisson, we present a two approximation for the first problem using Graham's rule, and observe that polynomial time approximation schemes can be obtained for the last two problems. If the jobs are all exponential, we present polynomial time approximation schemes for all three problems. We also obtain quasi-polynomial time approximation schemes for the last two problems if the jobs are Bernoulli variables.

A genetic algorithm approach to a general category project scheduling problem

Abstract: A genetic algorithm (GA) approach is proposed for the general resource-constrained project scheduling model, in which activities may be executed in more than one operating mode, and renewable as well as nonrenewable resource constraints exist. Each activity's operation mode has a different duration and requires different amounts of renewable and nonrenewable resources. The objective is the minimization of the project duration or makespan. The problem under consideration is known to be one of the most difficult scheduling problems, and it is hard to find a feasible solution for such a problem, let alone the optimal one. The GA approach described in this paper incorporates problem-specific scheduling knowledge by an indirect chromosome encoding that consists of selected activity operating modes and an ordered set of scheduling rules. The scheduling rules in the chromosome are used in an iterative scheduling algorithm that constructs the schedule resulting from the chromosome. The proposed GA is denoted a hybrid GA (HGA) approach, since it is integrated with traditional scheduling tools and expertise specifically developed for the general resource-constrained project scheduling problem. The results demonstrate that HGA approach produces near-optimal solutions within a reasonable amount of computation time.

Scheduling multiprocessor tasks with genetic algorithms

Abstract: In the multiprocessor scheduling problem, a given program is to be scheduled in a given multiprocessor system such that the program's execution time is minimized. This problem being very hard to solve exactly, many heuristic methods for finding a suboptimal schedule exist. We propose a new combined approach, where a genetic algorithm is improved with the introduction of some knowledge about the scheduling problem represented by the use of a list heuristic in the crossover and mutation genetic operations. This knowledge-augmented genetic approach is empirically compared with a "pure" genetic algorithm and with a "pure" list heuristic, both from the literature. Results of the experiments carried out with synthetic instances of the scheduling problem show that our knowledge-augmented algorithm produces much better results in terms of quality of solutions, although being slower in terms of execution time.

A shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop

Abstract: We present a shifting bottleneck heuristic for minimizing the total weighted tardi- ness in a job shop. The method decomposes the job shop into a number of single-machine subproblems that are solved one after another. Each machine is scheduled according to the solution of its corresponding subproblem. The order in which the single machine subproblems are solved has a significant impact on the quality of the overall solution and on the time required to obtain this solution. We therefore test a number of different orders for solving the subprob- lems. Computational results on 66 instances with ten jobs and ten machines show that our heuristic yields solutions that are close to optimal, and it clearly outperforms a well-known dispatching rule enhanced with backtracking mechanisms. © 1999 John Wiley & Sons, Inc. Naval

Survey of Job Shop Scheduling Techniques

Abstract: The sections in this article are 1 Introduction 2 Mathematical Techniques 3 Dispatching Rules 4 Artificial Intelligence (AI) Techniques 5 Artificial Neural Networks 6 Neighborhood Search Methods 7 Fuzzy Logic 8 Swarm 9 Reactive Scheduling 10 Learning in Scheduling 11 Theory of Constraints 12 Summary and Conclusions

Better Bounds for Online Scheduling

Abstract: We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal et al. [ J. Comput. System Sci., 51 (1995), pp. 359--366] gave a deterministic online algorithm that is 1.986-competitive. Karger, Phillips, and Torng [ J. Algorithms, 20 (1996), pp. 400--430] generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms is equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923-competitive; for all $m\geq 2$. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852-competitive.

A genetic algorithm for flexible job-shop scheduling

Abstract: Genetic algorithms have been applied to the scheduling of job shops-a class of very complicated combinatorial optimization problems. Among these algorithms for job shops, a common assumption is that the routes that jobs visit machines are fixed, this is not true for flexible job shops such as flexible manufacturing systems, where jobs have machine route flexibility. The paper presents a new genetic algorithm to solve the flexible job-shop scheduling problem with makespan criterion. The representation of solutions for the problem by chromosomes consists of two parts. The first part defines the routing policy and the second part the sequence of the operations on each machine. Genetic operators are introduced and used in the reproduction process of the algorithm. Numerical experiments show that our algorithm can find out high-quality schedules.

Statistical prediction of task execution times through analytic benchmarking for scheduling in a heterogeneous environment

Abstract: In this paper, a method for estimating task execution times is presented in order to facilitate dynamic scheduling in a heterogeneous metacomputing environment. Execution time is treated as a random variable and is statistically estimated from past observations. This method predicts the execution time as a function of several parameters of the input data and does not require any direct information about the algorithms used by the tasks or the architecture of the machines. Techniques based upon the concept of analytic benchmarking/code profiling are used to characterize the performance differences between machines, allowing observations from dissimilar machines to be used when making a prediction. Experimental results are presented which use actual execution time data gathered from 16 heterogeneous machines.

Genetic algorithms in integrated process planning and scheduling

Abstract: Process planning and scheduling are actually interrelated and should be solved simultaneously. Most integrated process planning and scheduling methods only consider the time aspects of the alternative machines when constructing schedules. The initial part of this paper describes a genetic algorithm (GA) based algorithm that only considers the time aspect of the alternative machines. The scope of consideration is then further extended to include the processing capabilities of alternative machines, with different tolerance limits and processing costs. In the proposed method based on GAs, the processing capabilities of the machines, including processing costs as well as number of rejects produced in alternative machine are considered simultaneously with the scheduling of jobs. The formulation is based on multi-objective weighted-sums optimization, which are to minimize makespan, to minimize total rejects produced and to minimize the total cost of production. A comparison is done w ith the traditional sequential method and the multi-objective genetic algorithm (MOGA) approach, based on the Pareto optimal concept.

A Graph-Theoretic Decomposition of the Job Shop Scheduling Problem to Achieve Scheduling Robustness

Abstract: In this paper we study the weighted tardiness job-shop scheduling problem, taking into consideration the presence of random shop disturbances. A basic thesis of the paper is that global scheduling performance is determined primarily by a subset of the scheduling decisions to be made. By making these decisions in an a priori static fashion, which maintains a global perspective, overall performance efficiency can be achieved. Further, by allowing the remaining decisions to be made dynamically, flexibility can be retained in the schedule to compensate for unforeseen system disturbances. We develop a decomposition method that partitions job operations into an ordered sequence of subsets. This decomposition identifies and resolves a "crucial subset" of scheduling decisions through the use of a branch-and-bound algorithm. We conduct computational experiments that demonstrate the performance of the approach under deterministic cases, and the robustness of the approach under a wide range of processing time perturbations. We show that the performance of the method is superior, particularly for low to medium levels of disturbances.

Provably efficient scheduling for languages with fine-grained parallelism

Abstract: Many high-level parallel programming languages allow for fine-grained parallelism. As in the popular work-time framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A common concern in executing such programs is to schedule tasks to processors dynamically so as to minimize not only the execution time, but also the amount of space (memory) needed. Without careful scheduling, the parallel execution on p processors can use a factor of p or larger more space than a sequential implementation of the same program.This paper first identifies a class of parallel schedules that are provably efficient in both time and space. For any computation with w units of work and critical path length d, and for any sequential schedule that takes space s1, we provide a parallel schedule that takes fewer than w/p + d steps on p processors and requires less than s1 + p·d space. This matches the lower bound that we show, and significantly improves upon the best previous bound of s1·p spaces for the common case where d«s1.The paper then describes a scheduler for implementing high-level languages with nested parallelism, that generates schedules in this class. During program execution, as the structure of the computation is revealed, the scheduler keeps track of the active tasks, allocates the tasks to the processors, and performs the necessary task synchronization. The scheduler is itself a parallel algorithm, and incurs at most a constant factor overhead in time and space, even when the scheduling granularity is individual units of work. The algorithm is the first efficient solution to the scheduling problem discussed here, even if space considerations are ignored.

Efficient approximation algorithms for scheduling malleable tasks

Abstract: A malleable task is a computational unit which may be executed on any arbitrary number of processors, its execution time depend- ing on the amount of resources allotted to it. According to the standard behavior of parallel applications, we assume that the mal- leable tasks are monotonic, i.e. that the execution time is decreas- ing with the number of processors while the computational work increases. This paper presents a new approach for scheduling a set of independent malleable tasks which leads to a worst case guar- antee of for the minimization of the parallel execution time, or makespan. It improves all other existing practical results includ- ing the two-phases method introduced by Turek et al. The main idea is to transfer the difficulty of a two phases method from the scheduling part to the allotment selection. We show how to formu- late this last problem as a knapsack optimization problem. Then, the scheduling problem is solved by a dual-approximation which leads to a simple structure of two consecutive shelves.

A genetic algorithm methodology for complex scheduling problems

Abstract: This paper considers the scheduling problem to minimize total tardiness given multiple machines, ready times, sequence dependent setups, machine downtime and scarce tools. We develop a genetic algorithm based on random keys representation, elitist reproduction, Bernoulli crossover and immigration type mutation. Convergence of the algorithm is proved. We present computational results on data sets from the auto industry. To demonstrate robustness of the approach, problems from the literature of different structure are solved by essentially the same algorithm.

Tabu Search Algorithms and Lower Bounds for the Resource-Constrained Project Scheduling Problem

Abstract: We present two tabu search algorithms for the resource-constrained project scheduling problem. Given are n activities which have to be processed without preemptions. During the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited. Furthermore, finish-start precedence relations between the activities are given. The objective is to determine a schedule with minimal makespan. The first tabu search approach relies on elimination of critical arcs and list-scheduling techniques. The second neighborhood is based on schedule schemes, where neighbors are generated by placing activities in parallel or deleting a parallelity relation. Furthermore, a column-generation approach for a linear programming-based lower bound is presented and computational results are reported.